On an asymptotic method in enumeration
Journal of Combinatorial Theory Series A
A bivariate asymptotic expansion of coefficients of powers of generating functions
European Journal of Combinatorics
Systems of functional equations
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Boltzmann Samplers for the Random Generation of Combinatorial Structures
Combinatorics, Probability and Computing
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
Enumeration and limit laws for series-parallel graphs
European Journal of Combinatorics
Maximal biconnected subgraphs of random planar graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Analytic Combinatorics
Random Trees: An Interplay between Combinatorics and Probability
Random Trees: An Interplay between Combinatorics and Probability
The degree sequence of random graphs from subcritical classes†
Combinatorics, Probability and Computing
Uniform random sampling of planar graphs in linear time
Random Structures & Algorithms
Vertices of given degree in series-parallel graphs
Random Structures & Algorithms
Degree distribution in random planar graphs
Journal of Combinatorial Theory Series A
On graphs with few disjoint t-star minors
European Journal of Combinatorics
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We present a unified general method for the asymptotic study of graphs from the so-called subcritical graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works in both the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number $g_n/n!$ (resp., $g_n$) of labelled (resp., unlabelled) graphs on $n$ vertices from a subcritical graph class ${\mathcal{G}}=\cup_n {\mathcal{G}_n}$ satisfies asymptotically the universal behavior $g_n = c \!n^{-5/2} \!\gamma^n \! (1+o(1))$ for computable constants $c,\gamma$, e.g., $\gamma\approx 9.38527$ for unlabelled series-parallel graphs, and that the number of vertices of degree $k$ ($k$ fixed) in a graph chosen uniformly at random from $\mathcal{G}_n$ converges (after rescaling) to a normal law as $n\to\infty$.